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Title: Solution Structure of Multi-layer Neural Networks with Initial Condition
Authors: 班榮超
Ban, Jung-Chao
Chang, Chih-Hung
Contributors: 應數系
Keywords: Initial value problem;Cellular neural networks;Sofic shift;Path set
Date: 2016-03
Issue Date: 2020-05-27 09:02:17 (UTC+8)
Abstract: This paper studies the initial value problem of multi-layer cellular neural networks. We demonstrate that the mosaic solutions of such system is topologically conjugated to a new class in symbolic dynamical systems called the path set (Abram and Lagarias in Adv Appl Math 56:109–134, 2014). The topological entropies of the solution, output, and hidden spaces of a multi-layer cellular neural network with initial condition are formulated explicitly. Also, a sufficient condition for whether the mosaic solution space of a multi-layer cellular neural network is independent of initial conditions is addressed. Furthermore, two spaces exhibit identical topological entropy if and only if they are finitely equivalent.
Relation: Journal of Dynamics and Differential Equations, Vol.28, No.1, pp.69-92
Data Type: article
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